| Title:
|
A short note on Perez’s approximation by dependence structure simplification (English) |
| Author:
|
Jiroušek, Radim |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
43 |
| Issue:
|
5 |
| Year:
|
2007 |
| Pages:
|
649-656 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Perez’s approximations of probability distributions by dependence structure simplification were introduced in 1970s, much earlier than graphical Markov models. In this paper we will recall these Perez’s models, formalize the notion of a compatible system of elementary simplifications and show the necessary and sufficient conditions a system must fulfill to be compatible. For this we will utilize the apparatus of compositional models. (English) |
| Keyword:
|
approximation of probability distributions |
| Keyword:
|
dependence structure simplification |
| Keyword:
|
compatibility |
| Keyword:
|
compositional models |
| MSC:
|
62E17 |
| MSC:
|
68T30 |
| idZBL:
|
Zbl 1148.68494 |
| idMR:
|
MR2376329 |
| . |
| Date available:
|
2009-09-24T20:27:58Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135804 |
| . |
| Reference:
|
[1] Jiroušek R.: Composition of probability measures on finite spaces.In: Proc. 13th Conf. Uncertainty in Artificial Intelligence UAI’97 (D. Geiger and P. P. Shenoy, eds.), Morgan Kaufmann, San Francisco 1997, pp. 274–281 |
| Reference:
|
[2] Jiroušek R.: Marginalization in composed probabilistic models.In: Proc. 16th Conf. Uncertainty in Artificial Intelligence UAI’00 (C. Boutilier and M. Goldszmidt, eds.), Morgan Kaufmann, San Francisco 2000, pp. 301–308 |
| Reference:
|
[3] Perez A.: Information, $\varepsilon $-sufficiency and data reduction problems.Kybernetika 1 (1965), 297–323 MR 0205410 |
| Reference:
|
[4] Perez A.: Information theory methods in reducing complex decision problems.In: Trans. 4th Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (J. Kožešník, ed.), Academia, Prague 1965, pp. 55–87 MR 0216676 |
| Reference:
|
[5] Perez A.: $\varepsilon $-admissible simplification of the dependence structure of a set of random variables.Kybernetika 13 (1977), 439–449 MR 0472224 |
| Reference:
|
[6] Somol P., Novovičová, J., Pudil P.: Notes on the evolution of feature selection methodology.Kybernetika 43 (2007), 713–730 Zbl 1134.62041, MR 2376333 |
| . |
